You say you “extracted a receive address.” Did you create this address with the BTG Core Wallet, or some other way?
Syncing the wallet and creating an address pair are two separate things.
Creating an address pair generates a public key (wallet address) and private key together; if you have a wallet address, it was created with a private key. If you created it with the Bitcoin Gold Core Wallet, it will have been stored in the wallet.dat file, which may be password-protected (if you opted for password protection.) This is true regardless of sync status or failure. The wallet software does not present you with the private key unless you explicitly try to pull it out, but it makes the public wallet address fairly easy to see.
As a separate matter, the wallet software will also sync with the public blockchain. This allows the wallet software to be aware of the current balance of addresses on the chain; without this, the wallet software can’t know how much is in your wallet address. If your sync fails or is restarted, the software doesn’t know what your current balance is, but that does not affect which address and keys the software has stored.
If you wish to, you can check the current balance of your public wallet address any time by entering it in a BTG blockchain explorer, such as ours.